Question 6

Explanation

We are given the function $f(x) = 2x - 3$ and the composite function $(g \circ f)(x) = 4x^2 - 12x + 10$. We are asked to find the value of $g(1)$.

The definition of a composite function is $(g \circ f)(x) = g(f(x))$. Let $u = f(x) = 2x - 3$. We rearrange this equation to express $x$ in terms of $u$:

Substitute $x$ into the equation $(g \circ f)(x)$:

Thus, we have $g(x) = x^2 + 1$.

Then the value of $g(1)$ is:

So, the value of $g(1)$ is $2$.